Top

Published in:

2019 | OriginalPaper | Chapter

6. Hypothesis Testing and ANOVA

Authors : Marko Sarstedt, Erik Mooi

Published in: A Concise Guide to Market Research

Publisher: Springer Berlin Heidelberg

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

We first describe the essentials of hypothesis testing and how testing helps make critical business decisions of statistical and practical significance. Without using difficult mathematical formulas, we discuss the steps involved in hypothesis testing, the types of errors that may occur, and provide strategies on how to best deal with these errors. We also discuss common types of test statistics and explain how to determine which type you should use in which specific situation. We explain that the test selection depends on the testing situation, the nature of the samples, the choice of test, and the region of rejection. Drawing on a case study, we show how to link hypothesis testing logic to empirics in SPSS. The case study touches upon different test situations and helps you interpret the tables and graphics in a quick and meaningful way.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

previous chapter Descriptive Statistics

next chapter Regression Analysis

In experimental studies, if respondents were paired with others (as in a matched case control sample), each person would be sampled once, but it still would be a paired sample.

The exact calculation of this test is shown on https://www.ibm.com/support/knowledgecenter/en/SSLVMB_20.0.0/com.ibm.spss.statistics.help/alg_npar_tests_mannwhitney.htm

The fundamental difference between the z- and t-distributions is that the t-distribution is dependent on sample size n (which the z-distribution is not). The distributions become more similar with larger values of n.

To obtain the critical value, you can also use the TINV function provided in Microsoft Excel, whose general form is “TINV(α, df).” Here, α represents the desired Type I error rate and df the degrees of freedom. To carry out this computation, open a new Excel spreadsheet and type in “ = TINV(2*0.025,9).” Note that we have to specify “2*0.025” (or, directly 0.05) under α, because we are applying a two-tailed instead of a one-tailed test.

Unfortunately, there is some confusion about the difference between the α and p-value. See Hubbard and Bayarri (2003) for a discussion.

Note that this is convention and most textbooks discuss hypothesis testing in this way. Originally, two testing procedures were developed, one by Neyman and Pearson and another by Fisher (for more details, see Lehmann 1993). Agresti and Finlay (2014) explain the differences between the convention and the two original procedures.

Note that this rule doesn't always apply such as for exact tests of probabilities.

We don’t have to conduct manual calculations and tables when working with SPSS. However, we can calculate the p-value using the TDIST function in Microsoft Excel. The function has the general form “TDIST(t, df, tails)”, where t describes the test value, df the degrees of freedom, and tails specifies whether it’s a one-tailed test (tails = 1) or two-tailed test (tails = 2). Just open a new spreadsheet for our example and type in “ = TDIST(2.274,9,1)”. Likewise, there are several webpages with Java-based modules (e.g., https://graphpad.com/quickcalcs/pvalue1.cfm) that calculate p-values and test statistic values.

The number of pairwise comparisons is calculated as follows: k·(k − 1)/2, with k the number of groups to compare.

In fact, these two assumptions are interrelated, since unequal group sample sizes result in a greater probability that we will violate the homogeneity assumption.

SS is an abbreviation of “sum of squares,” because the variation is calculated using the squared differences between different types of values.

Note that the group-specific sample size in this example is too small to draw conclusions and is only used to show the calculation of the statistics.

Note that when initiating the analysis by going to ► Analyze ► General Linear Model ► Univariate, we can request these statistics under Options (Estimates of effect size).

Agresti, A., & Finlay, B. (2014). Statistical methods for the social sciences (4th ed.). London: Pearson.

Benjamin, D. J., et al. (2018). Redefine statistical significance. Nature Human Behaviour, 2, 6–10.

Boneau, C. A. (1960). The effects of violations of assumptions underlying the t test. Psychological Bulletin, 57(1), 49–64.CrossRef

Cohen, J. (1992). A power primer. Psychological Bulletin, 112(1), 155–159.CrossRef

Everitt, B. S., & Skrondal, A. (2010). The Cambridge dictionary of statistics (4th ed.). Cambridge: Cambridge University Press.CrossRef

Field, A. (2013). Discovering statistics using SPSS (4th ed.). London: Sage.

Hubbard, R., & Bayarri, M. J. (2003). Confusion over measure of evidence (p’s) versus errors (α’s) in classical statistical testing. The American Statistician, 57(3), 171–178.CrossRef

Kimmel, H. D. (1957). Three criteria for the use of one-tailed tests. Psychological Bulletin, 54(4), 351–353.CrossRef

Lehmann, E. L. (1993). The Fischer, Neyman-Pearson theories of testing hypotheses: One theory or two? Journal of the American Statistical Association, 88(424), 1242–1249.CrossRef

Lakens, D., et al. (2018). Justify your alpha. Nature Human Behaviour, 2, 168–171.

Levene, H. (1960). Robust tests for equality of variances. In I. Olkin (Ed.) Contributions to probability and statistics (pp. 278–292). Palo Alto, CA: Stanford University Press.

Liao, T. F. (2002). Statistical group comparison. New York, NJ: Wiley-InterScience.CrossRef

Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50–60.CrossRef

Norman, G. (2010). Likert scales, levels of measurement and the “laws” of statistics. Advances in Health Sciences Education, 15(5), 625–632.CrossRef

Nuzzo, R. (2014). Scientific method: Statistical errors. Nature, 506(7487), 150–152.CrossRef

Ruxton, G. D., & Neuhaeuser, M. (2010). When should we use one-tailed hypothesis testing? Methods in Ecology and Evolution, 1(2), 114–117.CrossRef

Schuyler, W. H. (2011). Readings statistics and research (6th ed). London: Pearson.

Shapiro, S. S., & Wilk, M. B. (1965). An analysis of variance test for normality (complete samples). Biometrika, 52(3/4), 591–611.CrossRef

Van Belle, G. (2008). Statistical rules of thumb (2nd ed.). Hoboken, N.J.: John Wiley & Sons.CrossRef

Wasserstein, R. L., & Lazar, N. A. (2016). The ASA’s statement on p-values: Context, process, and purpose. The American Statistician, 70(2), 129–133.CrossRef

Welch, B. L. (1951). On the comparison of several mean values: An alternative approach. Biometrika, 38(3/4), 330–336.CrossRef

Kanji, G. K. (2006). 100 statistical tests (3rd ed.). London: Sage.CrossRef

Van Belle, G. (2011). Statistical rules of thumb (2nd ed.). Hoboken, N.J.: John Wiley & Sons.

Title: Hypothesis Testing and ANOVA
Authors: Marko Sarstedt
Erik Mooi
Publisher: Springer Berlin Heidelberg
Book: A Concise Guide to Market Research
Print ISBN: 978-3-662-56706-7

Electronic ISBN: 978-3-662-56707-4

Copyright Year: 2019
DOI: https://doi.org/10.1007/978-3-662-56707-4_6